We study the prospects of measuring the decay of the Higgs boson into a pair of muons at the International Linear Collider (ILC). The study is performed at center-of-mass energies of 250,GeV and 500,GeV, with fully-simulated Monte-Carlo samples based on the International Large Detector (ILD). The expected precision on cross section times branching ratio $sigma times mathrm{BR}(h to mu ^+ mu ^-)$ has been evaluated to be 24.9{%} for an integrated luminosity of 2,ab$^{-1}$ at 250,GeV. This result improves to 17.5{%} in combination with 4,ab$^{-1}$ of 500,GeV data. We also quantify the impact of the transverse momentum resolution on this analysis, and found that it is very important reach the design goal of an asymptotic resolution of $sigma_{1/P_t} = 2 times 10^{-5}$,GeV$^{-1}$.
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